---
title: Homomorphic Encryption in SemCom
url: https://www.emergentmind.com/topics/homomorphic-encryption-in-semcom
type: topic
---

# Homomorphic Encryption in SemCom

Homomorphic encryption in semantic communication (SemCom) defines a paradigm in which semantic representations—feature vectors or embeddings extracted from raw signals—are encrypted with schemes permitting algebraic manipulation directly on ciphertexts. This enables privacy-preserving end-to-end processing of semantic content, such as inference and aggregation, over untrusted channels or infrastructures. Approaches are grounded in both somewhat and fully homomorphic encryption (SHE/FHE). SemCom architectures require new cryptographic foundations, encoding methodologies, and algorithmic adaptations to achieve secure and semantically robust transmission of meaning, especially when deploying deep learning for joint source-channel coding.

## 1. Cryptographic Foundations for Homomorphic Encryption in SemCom

Homomorphic encryption (HE) schemes are characterized by their ability to support computation on encrypted data: given ciphertexts $c_1 = \text{Encrypt}(m_1)$ and $c_2 = \text{Encrypt}(m_2)$, one can compute $\text{Eval}_{\text{add}}(c_1, c_2)$ and $\text{Eval}_{\text{mult}}(c_1, c_2)$ such that decryption yields $m_1 + m_2$ and $m_1 \cdot m_2$, respectively.

Symmetric-key SHE
- The scheme of Dowerah & Krishnaswamy operates over $\mathbb{F}_q[x_1,\ldots,x_\ell]_{\leq r}$ (polynomials total degree $\leq r$). Ciphertexts are $n$-dimensional vectors in $\mathbb{F}_q^n$ constructed as $c = m p \cdot \mathbf{1} + G \mathbf{f} + \mathbf{e} \bmod q$, where $G$ encodes monomial evaluations at secret points and $\mathbf{e}$ is discrete-Gaussian noise. Homomorphic addition is vector addition; homomorphic multiplication is component-wise (Schur) product followed by scaling by $1/p$. The noise grows additively with additions, approximately squares with each multiplication, and correct decryption is possible if accumulated noise remains below a threshold [1902.05771].

Public-key FHE
- The Cheon–Kim–Kim–Song (CKKS) scheme, supporting approximate arithmetic over $\mathbb{R}^d$, is utilized for leveled FHE in SemCom [2501.10182]. CKKS enables efficient homomorphic addition/multiplication of encrypted feature vectors, permitting polynomial evaluation on real-valued semantic embeddings.

Security reductions define the trust boundaries: the multivariate polynomial SHE attains IND-CPA security reducible to the Hidden Subspace Membership (HSM) problem—distinguishing noisy subspace elements from random vectors—a generalization of Learning With Errors (LWE) [1902.05771].

## 2. Semantic Communication Architectures with Homomorphic Encryption

In SemCom, the communications stack is restructured as follows:

- Application-layer feature extraction: a semantic encoder maps the message $m$ to a feature vector $s \in \mathbb{R}^d$ (or $\mathbb{F}_q^\ell$).
- HE encryption: $c = \text{Encrypt}(pk, s)$, where $pk$ may be public or symmetric depending on the scheme.
- JSCC with encrypted input: a deep encoder $F_\text{enc}$ transforms $c$ into channel symbols $x = F_\text{enc}(c; \theta_\text{enc})$, suitable for transmission.
- Channel: the physical channel, often modeled as AWGN, adds noise.
- HE decryption and semantic decoding: the receiver reconstructs $c$ via $F_\text{dec}$, decrypts to estimate $s$, and uses a decoder $G_\text{dec}$ for the task output (e.g., classification, detection).

Notably, key modifications are required for deep JSCC models:
- Replace non-polynomial activations (ReLU, tanh) with polynomial ones, e.g., $f(x) = x^2$.
- Substitute max pooling with average pooling to ensure polynomial computability in HE [2501.10182].

## 3. Homomorphic Operations: Semantics-Preserving Functionalities

Homomorphic encryption makes possible a suite of semantic operations on ciphertexts, essential for end-to-end, privacy-preserving SemCom:

- **Feature aggregation:** Linear aggregation, e.g., weighted sums or averaging across encrypted features, uses homomorphic additions.
- **Similarity scoring:** Inner products between encrypted embeddings are realized by coordinate-wise homomorphic multiplication followed by summation.
- **Polynomial inference:** Elementwise non-linearities needed for shallow inference or low-degree neural activations can be implemented as polynomial maps over ciphertexts.

Mixed operations require careful control of noise parameters (e.g., $q$, $p$, standard deviation $\alpha$) and circuit depth—depth determines the number of successive adds/mults before decryption becomes unreliable due to noise growth [1902.05771]. In FHE settings, the CKKS scheme handles approximate polynomial maps, supporting deep learning tasks with quantized/floating-point features [2501.10182].

## 4. Integration Example: Semantic Keypoint Preservation and Deep JSCC

Empirical validation of semantics preservation under HE is demonstrated using the SIFT pipeline over encrypted images:

- Construction of DoG and Gaussian-blurred images is feasible over Paillier-encrypted images, as pixel-wise addition and subtraction are supported.
- Decrypting the ciphertext after SIFT-style homomorphic processing yields keypoints nearly identical to plaintext, indicating that semantic structural features survive through ciphertext-domain computation [2501.10182].

For deep learning-based SemCom, as in privacy-preserved deep JSCC, both encoding and decoding networks are constrained to polynomial operations (squares, average pooling, multiplications), allowing their execution on CKKS-encrypted feature vectors [2501.10182]. Quantitative evaluation shows that encrypted JSCC matches the plaintext JSCC classification accuracy within $0.02\%$–$0.05\%$ at high SNRs. However, computational time is significantly increased (e.g., $73.8$ s for encrypted versus $1.7 \times 10^{-4}$ s for plaintext processing on MNIST) [2501.10182].

### Example Table: Classification Accuracy by Method (MNIST, SNR 10dB)

| Model        | Classification Accuracy |
|--------------|------------------------|
| Separation (Model 1)        | 69.94 %           |
| Plaintext deep JSCC (Model 2)     | 91.13 %           |
| Plaintext privacy-preserved JSCC (Model 3) | 89.88 %           |
| HE-based privacy-preserved JSCC (Model 4)  | 89.60 %           |

## 5. Practical Considerations and Security Management

Practical deployment of HE in SemCom requires consideration of key management, efficiency, and operational viability:

- **Key update mechanisms:** Frequent key renewal (update interval $T$) is proposed to mitigate the risk of key compromise, balancing breach probability against throughput. Throughput decreases as update frequency increases, while security increases (overall breach probability over horizon $\mathcal{H}$ is $1 - (1 - P_{\text{break}}(T))^{\mathcal{H}/T}$) [2501.10182].
- **Noise management:** Strategies include modulus switching or scaling constants (e.g., increasing $p$) to bound cumulative noise and maintain decryptability [1902.05771].
- **Batching:** SIMD techniques pack multiple features into a single ciphertext (slot vectors), amplifying throughput for parallel operations.
- **Key distribution:** While symmetric-key SHE assumes secure out-of-band SK sharing, HE can be adapted to public-key scenarios using LWE-style key-switching.
- **Channel robustness:** The JSCC network is adapted to operate on ciphertext features; the removal of non-polynomial activations (e.g., ReLU$\to$x$^2$) is empirically shown to maintain semantic robustness at high SNR, with a 6–7% accuracy drop at low SNR shrinking as channel conditions improve [2501.10182].

## 6. Research Challenges and Future Directions

Key obstacles and research frontiers for homomorphic encryption in SemCom include:

- **Selective encryption**: Encrypting only semantic-critical portions of the signal (e.g., salient regions via object detection/segmentation) to reduce computational overhead without sacrificing security for crucial features.
- **Algorithmic optimization**: Using partially homomorphic schemes (e.g., Paillier) where only additions suffice, and algorithmic accelerations such as Montgomery modular multiplication.
- **Model compression and transfer**: Applying pruning, quantization, knowledge distillation, and transfer learning to neural JSCC under HE constraints.
- **Hardware acceleration**: Deploying homomorphic arithmetic on FPGAs, GPUs, or ASICs (e.g., NTT engines for CKKS) to address latency.
- **Robustness through adversarial training**: Exposing JSCC models to heterogeneous or perturbed ciphertexts during training to enhance resistance to both channel noise and adversarial manipulation.
- **Depth optimization**: Circuits are to be restricted in multiplicative depth suitable for the semantic task; bootstrapping and noise reduction are minimized to maximize efficiency.

A plausible implication is that advances in HE scheme efficiency and selective encryption aligned with semantic relevance are critical for scalable, real-time privacy preservation in semantic communication, especially in mobile or resource-constrained environments.

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References:  
Dowerah, Krishnaswamy, "A Somewhat Homomorphic Encryption Scheme based on Multivariate Polynomial Evaluation" [1902.05771]  
Zhou et al., "Secure Semantic Communication With Homomorphic Encryption" [2501.10182]

Source: https://www.emergentmind.com/topics/homomorphic-encryption-in-semcom